Separate tickets and rechecking luggage with 1hr 55 between flight is possible if everything works correctly but a short incoming flight delay, delayed baggage reclaim, missing a Heathrow Express train with 20 minute wait for the next etc makes the risk of missing conformance at T3 security a distinct possibility. You don't mention what cabin you are travelling in, whether you can use e-gate passport control, security fast track all of which influence transfer time.

Travelling hand baggage only would remove some of the risk plus would allow you to transfer terminals airside instead of landslide but even then there wouldn't be a large safety margin.

If you are relaxed with regards risk 1hr 55 does allow sufficient time but no margin. Heathrow transfers especially when transferring terminals isn't fast and that is without delays which are currently common. Personally I wouldn't feel comfortable travelling on separate tickets without atleast 3 hrs between flights.